Impacts of noise on a field theoretical model of the human brain

Salient properties of the spatio-temporal patterns in MEG recordings of human brain activity, such as macroscopic coherence of a limited number of modes and the occurrence of phase transitions, have been successfully described with the help of field theoretical models for the dendritic currents in the cortex. So far, however, these models have ignored the effects of noise which play an important role in the emergence of such properties. The present article provides a formal treatment of the effects of stochastic fluctuations in the vicinity of the phase transitions that were observed by Kelso in his so-called Julliard experiment [Fuchs et al., Phase transition in the human brain: spatial mode dynamics, Int. J. Bifurcation and Chaos 2 (1992) 917-939; H. Haken, Principles of Brain Functioning, Springer, Berlin, 1996; J.A.S. Kelso, Dynamic Patterns - The Self-organization of Brain and Behavior, MIT Press, Cambridge, 1995]. To describe and examine these effects, the field theoretical model proposed by Jirsa and Haken [A field theory of electromagnetic brain activity, Phys. Rev. Lett. 77 (1996) 960-963; A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics, Physica D 99 (1997) 503-526] was extended by incorporating Gaussian white noise. The extended model describes the stochastic properties of the most dominant spatio-temporal components, including stochastic variations of the amplitudes of the extracted spatial modes. Furthermore, the model captures critical phenomena such as critical slowing down and critical fluctuations, which are derived analytically. These theoretical results are generalized by means of numerical simulations of amplitude and phase dynamics. (C) 1998 Elsevier Science B.V. All rights reserved.